The Shulhan Aruch (Orah Haim 133:1) states that on Shabbat and Yom Tov, “Barechu” is not recited after the last Kaddish. It is explained in Masechet Sofrim (10:7) that “Barechu” was instituted at the end of the prayer for those who may have missed its recital earlier in the prayer. The Zohar (Ruth, pg. 53) states that one who did not respond to “Barechu” will be afflicted with anger that day, and will have an unsettled Neshama. Furthermore, the response to “Barechu” (ie. “Baruch Hashem HaMevorach LeOlam Va’ed”) is made up of five words, corresponding to the five levels of the soul. The Arizal (Pri Etz Haim, Sha’ar Keriat Shema, ch. 1) says that by responding, one allows one’s Neshama to settle in the proper place. Because of its benefits, the Sages instituted the recital of “Barechu” for those that did not hear it earlier.
The rationale of the Shulhan Aruch is that even if one arrives late on Shabbat or Yom Tov, one will still be able to hear “Barechu” when the Torah is read. Thus, there is no need to say it at the end of the prayer, and indeed, this is the approach of the Ashkenazic communtiy. Nevertheless, the Sephardic custom is to say “Barechu” before “Alenu Leshabe’ah” of Shaharit (and for that matter, Arvit) everyday of the week because of its Kabbalistic importance. It goes without saying that this only applies if there is a Minyan.
Summary: Reciting and responding to “Barechu” hasspiritualbenefits and is alwaysrecited at the end of Shaharitand Arvit.